Question 1: You have been asked by the government to estimate the recreational use value of a national wildlife park in your city that is home to many colorful birds as well as hundreds of Eucalyptus trees. To conduct your analysis, the government has provided you with information on all of the visits that were made last year. You group visits into five Zones based on the distance visitors traveled to arrive at the park and you collect population data for each Zone, giving you the following table: Zone Visits (V) Total Population Visits / 1,000 in Population (v) Distance (km) Travel Cost (T) 1 6,000 80,000 20 2 1.200 30 20,000 20,000 3 900 40 4 1,800 50 60,000 100,000 5 1,500 60 After learning more about the park and its visitors, you conclude that the appropriate trip- generating function is given by: v(T;,P) = a + B(T; +P) where v(T;,P) is the number of annual park visits taken per 1,000 people in the population from Zone i, T; is the travel cost of visiting the park incurred by individuals from Zone i, P is the park entrance fee (which is the same for everyone), and a and B are parameters to be estimated. When the data was collected, there was no fee to enter the park. You conclude that travel costs per kilometer are $1. Using this information, answer the following questions. Note: I'll refer to v(T;,P) as zone-specific population-adjusted demand (or trip-generating func- tion) and I'll refer to: V(T., P) = (a + B(T; + p) total population 1,000 as zone-specific total demand. Note the distinction between little v and big V. Part (a) The first step is to estimate the parameters of the trip-generating function, a and B, using the data that you've collected. What values for a and B best fit the data? What, then, is the estimated trip-generating function? Hint: To solve for a and B it may be useful to fill out the two blank columns in the above table.] Part (b) Using the estimated trip-generating function from Part (a) derive each Zone's population- adjusted demand for visits. (Hint: Travel costs are fixed for individuals residing within a partic- ular Zone. Therefore, each Zone's population-adjusted demand for visits (vi) will be a function of the park entrance fee (P) only.] Part (c) The choke price is the park entrance fee at which no one will choose to visit the park if they are charged anything equal to or above it. Since individuals from different Zones have different travel costs (T), chokes prices will also vary across Zones. Using your answer to Part (b), calculate the choke price for visitors from each Zone. Part (d) The next step is to determine the surrogate demand function for visits to the park, which relates the quantity of visits from all Zones combined (V) to the park admission fee (P). Illustrate the surrogate demand function on the below graph, making sure to numerically label any kinks in the demand curve. (Hint: This entails aggregating each Zone's total demand (not population-adjusted demand). To do this, you will want to combine Part (b) with the popu- lation data in the above table. The choke prices that you calculated in Part (c) will help you determine where the kinks are in the demand curve. Also, when aggregating, remember that demand cannot be negative. Part (e) You are now in a position to estimate the total recreational use value of the wildlife park. What is this value when the park entrance fee is $0? Illustrate this value on the graph from Part (d). o 10 30 0 P ($) 3,000 6,000 9,000 12,000 Question 1: You have been asked by the government to estimate the recreational use value of a national wildlife park in your city that is home to many colorful birds as well as hundreds of Eucalyptus trees. To conduct your analysis, the government has provided you with information on all of the visits that were made last year. You group visits into five Zones based on the distance visitors traveled to arrive at the park and you collect population data for each Zone, giving you the following table: Zone Visits (V) Total Population Visits / 1,000 in Population (v) Distance (km) Travel Cost (T) 1 6,000 80,000 20 2 1.200 30 20,000 20,000 3 900 40 4 1,800 50 60,000 100,000 5 1,500 60 After learning more about the park and its visitors, you conclude that the appropriate trip- generating function is given by: v(T;,P) = a + B(T; +P) where v(T;,P) is the number of annual park visits taken per 1,000 people in the population from Zone i, T; is the travel cost of visiting the park incurred by individuals from Zone i, P is the park entrance fee (which is the same for everyone), and a and B are parameters to be estimated. When the data was collected, there was no fee to enter the park. You conclude that travel costs per kilometer are $1. Using this information, answer the following questions. Note: I'll refer to v(T;,P) as zone-specific population-adjusted demand (or trip-generating func- tion) and I'll refer to: V(T., P) = (a + B(T; + p) total population 1,000 as zone-specific total demand. Note the distinction between little v and big V. Part (a) The first step is to estimate the parameters of the trip-generating function, a and B, using the data that you've collected. What values for a and B best fit the data? What, then, is the estimated trip-generating function? Hint: To solve for a and B it may be useful to fill out the two blank columns in the above table.] Part (b) Using the estimated trip-generating function from Part (a) derive each Zone's population- adjusted demand for visits. (Hint: Travel costs are fixed for individuals residing within a partic- ular Zone. Therefore, each Zone's population-adjusted demand for visits (vi) will be a function of the park entrance fee (P) only.] Part (c) The choke price is the park entrance fee at which no one will choose to visit the park if they are charged anything equal to or above it. Since individuals from different Zones have different travel costs (T), chokes prices will also vary across Zones. Using your answer to Part (b), calculate the choke price for visitors from each Zone. Part (d) The next step is to determine the surrogate demand function for visits to the park, which relates the quantity of visits from all Zones combined (V) to the park admission fee (P). Illustrate the surrogate demand function on the below graph, making sure to numerically label any kinks in the demand curve. (Hint: This entails aggregating each Zone's total demand (not population-adjusted demand). To do this, you will want to combine Part (b) with the popu- lation data in the above table. The choke prices that you calculated in Part (c) will help you determine where the kinks are in the demand curve. Also, when aggregating, remember that demand cannot be negative. Part (e) You are now in a position to estimate the total recreational use value of the wildlife park. What is this value when the park entrance fee is $0? Illustrate this value on the graph from Part (d). o 10 30 0 P ($) 3,000 6,000 9,000 12,000